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MMO 219 Moscow MO 1952 (1-x)^n + (1 + x)^n < 2^n if n>= 2, |x| < 1

Source:

August 8, 2019

inequalitiesalgebra

Problem Statement

Prove that

(1 - x)^n + (1 + x)^n < 2^n

for an integer

n \ge 2

and

|x| < 1